An unusual inequality condition

Consider all triples of non-zero real numbers that satisfy

$\left| \frac { 1 }{ a } \right| +\left| \frac { 1 }{ b } \right| +\left| \frac { 1 }{ c } \right| \le 3$

What is the minimum value of

${(a^2+4(b^2+c^2))(b^2+4(a^2+c^2))(c^2+4(a^2+b^2)) ?}$